What is simplify-log_{10}(2.6*10^{-7}) ?

The solution to simplify-log_{10}(2.6*10^{-7}) is -log_{10}(2.6)+7

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simplify-log_{10}(2.6*10^{-7})

simplify

- lo g_{10} (2.6 \cdot 1 0^{- 7})

- lo g_{10} (2.6) + 7

Decimal Notation

6.58502 \dots

Solution steps

- lo g_{10} (2.6 \cdot 1 0^{- 7})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (2.6 \cdot 1 0^{- 7}) = lo g_{10} (2.6) + lo g_{10} (1 0^{- 7})

= - (lo g_{10} (2.6) + lo g_{10} (1 0^{- 7}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (1 0^{- 7}) = - 7 lo g_{10} (10)

= - (lo g_{10} (2.6) - 7 lo g_{10} (10))

7 lo g_{10} (10) = 7

= - (lo g_{10} (2.6) - 7)

Distribute parentheses

= - (lo g_{10} (2.6)) - (- 7)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - lo g_{10} (2.6) + 7

ln (d) - ln (a \cdot b) + ln (c)

6 lo g_{7} (7 x + 1) + \frac{1}{4} lo g_{7} (x + 4)

- lo g_{10} (4.55 \cdot 1 0^{- 8})

- \frac{1}{6} \cdot lo g_{2} (\frac{1}{6}) - \frac{5}{6} \cdot lo g_{2} (\frac{5}{6})

5 ln (x + 4) - 8 ln (x)

What is simplify-log_{10}(2.6*10^{-7}) ?
The solution to simplify-log_{10}(2.6*10^{-7}) is -log_{10}(2.6)+7